How can one determine the order of the reaction? Well, the rate must be determined at several concentrations.

For the reaction above experiments reveal that

Experiment A. If the concetration of NO2 is 0.00895 M the rate at which the NO2 is consumed is 4.2 x 10-5 M/s

Experiment B. If the concetration of NO2 is 0.00515 M the rate at which the NO2 is consumed is 1.4 x 10-5 M/s

 

If we divide on reaction by the other the following expression results

Since k, the rate constant, only changes with changes in temperature the k's reduce to 1. The expression simplifies to
or
3 = 1.737x
To solve for x take the log (or ln) of wach side of the equation.

ln 3 = ln 1.737x

ln 3 = x ln 1.737

1.0986 = 0.5527 x

x = 1.99 => 2.0

We would say the reaction is second order in NO2 and the rate law is

So, what did we do?

 

Another example...

 

The rate at which FClO2 is formed depends on two reactants.

To determine the order with respect to each reactant we need to perform experiments that measure the effect of changing the concentration of one reactant at a time.

[F2]
[ClO2]
initial rate

-d[F2]/dt
0.10
0.010
1.2 x 10-3
0.10
0.040
4.8 x 10-3
0.20
0.010
2.4 x 10-3
 

the rate law is.....

To determine the order we need to find how the rate is effected by the change in the concentration of one reactant.

So, pick a pair of experimets where the concentration of one reactant changes, and the concentration of the other does not...that way the other concentration term cancels out...

0.50 = (0.50)x(1)y

0.50 = (0.50)x

x = 1

 

Repeat with another experiment where the concentration of the first reactant remains constant.

0.25 = 0.25y

y = 1

 

The rate law is...

The rate constant, k, can be found by substitution.

 

1.2 x 10-3 M/s = k (0.10 M)(0.010 M)

 

k = 1.2 M-1•s-1

The units of the rate constant, k, are determined by the order of the reaction.